gamma radiation is a photon and cannot make food radioactive because the energy is insufficient

for something to become radioactive it has to be unstable nucleus

think of water which has hydrogen and oxygen

water has stable hydrogen for it to become radioactive you have to add a neutron to the hydrogen to make deuterium which is unstable and is radioactive

a neutron is 0.1 nm in size vs a photon which is infinitely smaller (it has no mass)

the only possible way for gamma radiation to make a nucleus unstable is to knock out a neutron by exceeding the binding energy of the neutron

hydrogen, which has the lowest binding energy for its neutron of all the elements, requires 2 million electron volts to lose its neutron

the two isotopes used for food irradiation are cobalt 60 and cesium 137 the peak for co-60 is 1.3 Mev and for cs-137 the peak is 0.662 Mev

so the gammas dont have enough energy to make anything radioactive